Question

Water in a canal, 6 m wide and 1.5 m deep, is flowing at a speed of 4 km/hr. How much area will it irrigate in 10 minutes if 8 cm of standing water is needed for irrigation? [CBSE 2014]

Answer 1

$$\begin{gathered} \mathrm{We}\mathrm{have}, \\ \mathrm{Width}\mathrm{of}\mathrm{the}\mathrm{canal},b=6\mathrm{m}, \\ \mathrm{Depth}\mathrm{of}\mathrm{the}\mathrm{canal},h=1.5\mathrm{m}, \\ \mathrm{Height}\mathrm{of}\mathrm{the}\mathrm{standing}\mathrm{water}\mathrm{needed}\mathrm{for}\mathrm{irrigation},H=8\mathrm{cm}=0.08\mathrm{m}, \\ \mathrm{Speed}\mathrm{of}\mathrm{the}\mathrm{flowing}\mathrm{water},l=4\mathrm{km}/\mathrm{h}=\frac{4000}{60}=\frac{200}{3}\mathrm{m}/\min \\ \mathrm{Now}, \\ \mathrm{Volume}\mathrm{of}\mathrm{water}\mathrm{flowing}\mathrm{out}\mathrm{from}\mathrm{canal}\mathrm{in}1\min =lbh \\ =\frac{200}{3}\times 6\times 1.5 \\ =600{\mathrm{m}}^3 \\ \Rightarrow \mathrm{Volume}\mathrm{of}\mathrm{water}\mathrm{flowing}\mathrm{out}\mathrm{from}\mathrm{canal}\mathrm{in}10\min =600\times 10=6000{\mathrm{m}}^3 \\ \mathrm{So},\mathrm{the}\mathrm{area}\mathrm{of}\mathrm{irrigation}=\frac{\mathrm{Volume}\mathrm{of}\mathrm{water}\mathrm{flowing}\mathrm{out}\mathrm{from}\mathrm{canal}\mathrm{in}10\min }{\mathrm{Height}\mathrm{of}\mathrm{the}\mathrm{standing}\mathrm{water}\mathrm{needed}\mathrm{for}\mathrm{irrigation}} \\ =\frac{6000}{0.08} \\ =75000{\mathrm{m}}^2 \\ =7.5\mathrm{hectare}\left(\mathrm{As},1\mathrm{hectare}=10000{\mathrm{m}}^2\right) \end{gathered}$$

Hence, it will irrigate 7.5 hectare of area in 10 minutes.